Analog clocks have always annoyed me, so I decided to make my own. This is the logical solution I think. There's only one hand, which moves round once a day and shows where the sun is on the map. In the photo it is nearly 10pm in the UK so the sun is over the Alaska timezone. The 6am-6pm line is your horizon, so the top half is your daytime.
This one is for GMT/UTC - you'd need to rotate the map for different timezones, to put your location at the top under the noon marker.
The map is an azimuthal equal-area projection, made with NASA's G.Projector: http://www.giss.nasa.gov/tools/gprojector/
I bought a 24-hour clock and simply inserted the printed map in place, after removing the minute and second hands.